Firstly, the Forrest Mims books are still out there. He even has a fun website, for those interested in... um... almost everything you can imagine.
As for building stuff for practice, you can go in a lot of directions; certainly the Heath kits is one way. Also look at Solarbotics, Adafruit, Arduino, and Picaxe where I have had a lot of success finding things that are fun / educational / useful / all of the above. The modern way to make stuff work is to program a microcontroller to do a task, whereas in the past, people learned how to build their circuits with basic components and various IC's to achieve a specific result. I've been on the microcontroller road for a while, but along the way I learnedhow to add a few amplifiers and low-pass filters here and there, so I'm ahead on both counts now. I still don't like soldering together things that don't work, so I still spend a very long time designing and figuring things out to the Nth degree, even when building a second one would be faster.
For pure soldering practice, just pick up the blinking LED lapel pins or similar cheap educational kits. I've done a few; kids love them.
For a bit more theory, broken down into digestible chunks, visit
www.allaboutcircuits.com. There are others like it.
Great visualizations/animations/simulations of simple and complex circuits:
http://www.falstad.com/circuit/e-index.htmlIf you download the package you can write your own sims.